The principal would like to assemble a committee of 4 students from the 14-member student council. How many different committees can be chosen ?
This is a combination problem since the order of the students in the committee does not matter.
The number of ways to choose a committee of 4 students from a group of 14 students is given by the combination formula:
C(n, k) = n! / k!(n-k)!
Where n is the total number of students (14) and k is the number of students in the committee (4).
Plugging in the values:
C(14, 4) = 14! / 4!(14-4)!
C(14, 4) = 14! / 4!10!
C(14, 4) = (14*13*12*11) / (4*3*2*1)
C(14, 4) = 1001
Therefore, there are 1001 different committees that can be chosen from the 14-member student council.